Robust sparsity-preserved learning with application to image visualization

摘要

Linear subspace learning is of great importance for the purpose of visualization of high-dimensional observations. Sparsity-preserved learning (SPL) is a recently developed technique for linear subspace learning. Its objective function is formulated by using the \(\ell _2\)-norm, which implies that the obtained projection vectors are likely to be distorted by outliers. In this paper, we develop a new SPL algorithm called SPL-L1 based on the \(\ell _1\)-norm instead of the \(\ell _2\)-norm. The proposed approach seeks projection vectors by minimizing a reconstruction error subject to a constraint of samples dispersion, both of which are defined using the \(\ell _1\)-norm. As a robust alternative, SPL-L1 works well in the presence of atypical samples. We design an iterative algorithm under the framework of bound optimization to solve the projection vectors of SPL-L1. The experiments on image visualization demonstrate the superiority of the proposed method.